How do you write $3^{- \frac{3}{2}}$ $3^(−3/2)$ exponential expression in radical form?

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Answer 1 · 2016-01-10T23:25:23

$\frac{1}{\sqrt{27}}$ $1/sqrt27$

Using the following 'laws of indices'

$a^{- m} = \frac{1}{a^{m}} and a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ $a^-m = 1/a^m and a^(m/n) = root(n)(a^m)$

rewrite with a positive index

$3^{- \frac{3}{2} = \frac{1}{3^{\frac{3}{2}}}}$ $3^(-3/2 = 1/3^(3/2 )$

now $3^{\frac{3}{2}} = \sqrt{3^{3}} = \sqrt{27}$ $3^(3/2) = sqrt(3^3) = sqrt27$

$\Rightarrow 3^{- \frac{3}{2}} = \frac{1}{\sqrt{27}}$ $rArr 3^(-3/2) = 1/sqrt27$

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